Monopolistic Behavior

Capturing Surplus

• First-Degree Price Discrimination: Making the Most from Each Consumer

• Second-Degree Price Discrimination: Quantity Discounts

• Third-Degree Price Discrimination: Different Prices for Different Market Segments

• Tying (Tie-In Sales), Bundling

• Advertising

Uniform Price Vs. Price Discrimination

• A monopolist charges a uniform price if it sets the same price for every unit of output sold

• While the monopolist captures profits due to an optimal uniform pricing policy

  • It does not receive the consumer surplus or dead-weight loss associated with this policy

• A firm with market power may be able to increase its profits by charging more than one price for its product through price discrimination

Forms of Price Discrimination

• A policy of first-degree (or perfect) price discrimination prices each unit sold at the consumer’s maximum willingness to pay

  • This willingness to pay is directly observable by the monopolist

• A policy of second-degree price discrimination allows the monopolist to offer consumers a quantity discount

  • Two part tariffs

• A policy of third-degree price discrimination offers a different price for each segment of the market (or each consumer group) when membership in a segment can be observed

Conditions

Certain market features must be present for a firm to capture more surplus with price discrimination:

1. A firm must have some market power to price-discriminate
   • the demand curve the firm faces must be downward sloping
   • If the firm is a price taker it cannot set different prices for different units of output

Conditions

2. The firm must have some information about the different amounts people will pay for its product
   • reservation prices or elasticities of demand across consumers
3. A firm must be able to prevent resale or arbitrage
   • A reseller might capture the surplus instead of the firm

Willingness to Pay Curve

• The demand curve is the willingness to pay curve

• Since the demand curve slopes downward, the consumer buying the first unit is willing to pay a higher price than the consumer buying the second unit

• If the seller can perfectly implement first-degree price discrimination, it will price each unit at the maximum amount the consumer of that unit is willing to pay

Uniform Price Vs. Price Discrimination

Pareto Efficiency

• The producer sells each unit to the consumer with the highest reservation price for that unit, at that price

• The monopolist will continue selling units until the reservation price exactly equals the marginal cost

• The producer captures all the surplus and there is no deadweight loss

• Perfect first-degree price discrimination therefore leads to an economically efficient level of output!

Caveats

• In the real world, it is harder to learn about willingness to pay

• If you ask a customer about her willingness to pay, she will not reveal her reservation price

  • A consumer would like to tell you that she has a low willingness to pay so that she can capture some consumer surplus herself

Caveats

• Often sellers can learn something about willingness to pay based on
  • knowledge of where a person lives and works,
  • how she dresses or speaks,
  • the kind of car she drives, or
  • how much money she makes
• The information may not perfectly reveal a consumer’s willingness to pay, but it can help the seller to capture more surplus than it could without such information

Uniform vs. 1st Degree Pricing

Marginal Revenue Curve

• With uniform pricing, \(MR=P+\frac{dP}{dQ}Q\)

• With perfect first-degree price discrimination, only the first effect is present

• When the firm sells one more unit, it does not have to reduce its price on all the other units it is already selling

• So the marginal revenue curve with first-degree price discrimination is just \(MR = P\)

• The marginal revenue curve equals the demand curve

Second Degree Price Discrimination

• A policy of second-degree price discrimination allows the monopolist to charge a different price to different consumers

• While different consumers pay different prices, the reservation price of any one consumer cannot be directly observed

Second Degree Price Discrimination

• Sellers know that each customer’s demand curve for a good is typically downward-sloping

  • the customer’s willingness to pay decreases as successive units are purchased

• A seller may use this information to capture extra surplus by offering quantity discounts to consumers

• Not every form of quantity discounting represents price discrimination. Often sellers offer quantity discounts because it costs them less to sell a larger quantity

Second Degree Price Discrimination

• One distinguishing feature of second-degree price discrimination is that the amount consumers pay for the good or service actually depends on two or more prices (parts)

• For example, telecommunication services work under a multipart tariff: a subscription charge plus a usage charge

Block Tariff

• If a consumer pays one price for one block of output and another price for another block of output, the consumer faces a block tariff

• Firm’s objective is to maximize profits by choosing the optimizing quantity at each block (therefore looking for the optimal block price)

Block Tariff

Block Tariff

Show mathematically on the board

Average Outlay

Consumer’s average expenditure, average outlay, is total expenditure \(E\) divided by total quantity \(Q\)

In our previous example, \[ E = \begin{cases} \$14Q, & \text{if } Q \leq 6 \\ \$84 + \$8(Q-6), & \text{if } Q > 6 \end{cases} \]

So, the consumer’s average outlay is \[ \frac{E}{Q} = \begin{cases} \$14, & \text{if } Q \leq 6 \\ \frac{\$84 + \$8(Q-6)}{Q}, & \text{if } Q > 6 \end{cases} \]

Average Outlay

Self Select

• The problem with first-degree price discrimination is that the high-willingness-to-pay person may pretend to be the low-willingness-to-pay person
  • The seller might not tell them apart effectively
• By offering two different price-quantity packages in the market,
  • one targeted to the high-demand and the other targeted to the low-demand person,
  • the seller might induce the consumers to choose the package meant for them: self select

Self Select

Subscription and Usage Tariff

• A monopolist charges a two-part tariff if it charges a per unit fee, \(r\), plus a lump sum fee (paid whether or not a positive number of units is consumed), \(F\)

\[ T=F+rQ \]

• This, effectively, charges demanders of a low quantity a different average price than demanders of a high quantity

• Example: include hook-up charge plus usage fee for a telephone, club membership, and so on

Subscription and Usage Tariff

• All customers are identical

  • P = 100 - Q

  • MC = AC = 10

• What is the optimal two-part tariff?

• Two steps: Draw graph on the board

  • Maximize the benefits to the consumers by charging r = MC = 10

  • Capture this benefit by setting F = consumer benefits = 4050

Subscription and Usage Tariff

• Any higher usage charge would result in a dead-weight loss that could not be captured by the monopolist

• Any lower usage charge would result in selling at less than marginal cost

• In essence, the monopolist maximizes the surplus, then sets the lump sum fee to capture the entire surplus for itself

• The total surplus captured is the same as in the case of perfect price discrimination

In the Real World

• In the real world, the firm cannot so easily capture all the surplus, for two reasons:

1. Demand differs from one consumer to the next. High subscription and usage tariffs might capture more surplus from large-demand consumers, but small-demand consumers will not buy the service at all

2. The firm cannot tell apart large from small-demand consumers. Firms need to offer customers a menu of subscription and usage charges to incentivize them to self-select

Third Degree Price Discrimination

• If a firm can identify different consumer groups, or segments, in a market and can estimate each segment’s demand curve, the firm can practice third-degree price discrimination by setting a profit-maximizing price for each segment

• Example: Movie ticket sales to senior citizens or students at a discount

• How does a monopolist maximize profit with this type of price discrimination?

Third Degree Price Discrimination

The optimal pricing maximizes the monopolist’s profits \[ \max_{Q_1,Q_2} P_1(Q_1)Q_1 + P_2(Q_2)Q_2- C(Q_1+Q_2) \]

\(P_i(Q_i)\) denote the inverse demand curves of group \(i\)

Third Degree Price Discrimination: Optimal Pricing

The optimal solution must have \[ \begin{aligned} MR_1(Q_1)&=MC(Q_1+Q_2) \\ MR_2(Q_2)&=MC(Q_1+Q_2) \end{aligned} \]

• The marginal cost of producing an extra unit of output must be equal to the marginal revenue in each market

Third Degree Price Discrimination: Optimal Pricing

• In other words, the monopolist maximizes total profits by maximizing profits from each group individually

• Since marginal cost is the same in each market, \(MR_1=MR_2=MC\)

• Otherwise, the monopolist could raise revenues by switching sales from the low MR group to the high MR group

Third Degree Price Discrimination

Third Degree Price Discrimination

• Note that the price is higher in the lower elasticity demand than in the high elasticity demand

• A firm that price discriminates will set a low price for the price-sensitive group and a high price for the group that is relatively price-insensitive

• Senior citizens and students are more likely to be price-sensitive than the average consumer

Third Degree Price Discrimination

\[ \begin{aligned} P_1\left(1-\frac{1}{ |\epsilon_{Q_1,P_1}| }\right)&=MC(Q_1+Q_2) \\ P_2\left(1-\frac{1}{ |\epsilon_{Q_2,P_2}| }\right)&=MC(Q_1+Q_2) \end{aligned} \]

if \(P_1>P_2\), then we must have

\[ \begin{aligned} 1-\frac{1}{ |\epsilon_{Q_1,P_1}| } &< 1-\frac{1}{ |\epsilon_{Q_2,P_2}| } \\ \implies |\epsilon_{Q_2,P_2}| &> |\epsilon_{Q_1,P_1}| \end{aligned} \]

The market with the higher price must have the lower price elasticity of demand.

Screening

Sorting consumers based on a consumer characteristic that

1. is observable by the firm (age,status) and

2. strongly related to a consumer unobserved characteristic that the firm would like to know (willingness to pay; elasticity of demand)

• Screening Mechanisms:

  • Intertemporal Price Discrimination (Telephone, highest during peak demand, daytime)
  • Coupons and Rebates (People who collect coupons is likely to be more price-sensitive)

Implementing Price Discrimination

• Problem: High-demand consumers might buy at a price targeting low-demand consumers Ex.: Coupons easily available to everyone

• How can the firm ensure that

  • consumers who are targeted to pay the high price, pay the high price; and
  • consumers who are targeted to pay the low price, pay the low price?

Example

Example

Building a Fence

• Keep the less price-sensitive consumers from being able and/or willing to purchase the low-price version of the good

• Beta consumers are better off; they prefer C rather than B. They also prefer C to A

• Alpha consumers prefer A to C. Thus, they will purchase the high-price high-quality version

• By reducing the quality of the low-price offer, the firm makes the low-price version unattractive for alpha consumers

  • Beta consumers are more tolerant of quality degradations, they choose the low-quality version

Versioning

• A strategy of selling two (or more) versions of the product with different quality levels at different prices

• Damaged goods strategy, a firm creates a low-end version of its full-priced good by deliberately damaging the product

  • Removing features or reducing performance
  • Damaging the product might increase the marginal cost of producing the damaged good
  • The cost differential is worth incurring if the gain in profits, resulting from implementing the price discrimination scheme, is greater

Tying (Tie-in Sales)

• A sales practice that allows a customer to buy one product (the tying product) only if that customer agrees to buy another product (the tied product)

• Often, tying is used when customers differ by the frequency with which they wish to use a product

• Tying often enables a firm to extend its market power from the tying product to the tied product

Bundling

• A type of tie-in sale in which a firm requires customers who buy one of its products to simultaneously buy another of its products

• Bundling can increase profits when

  • customers have different tastes (different willingnesses to pay) for the two products and when
  • the firm cannot price discriminate

• But bundling does not always pay

Bundling: Negatively Correlated Preferences

• Without bundling: \(P_c = \$1500; P_m = \$600 ; Profit_{cm} = \$800\)

• With bundling: \(P_b = \$1800; Profit_b = \$1000\)

Bundling: Positively Correlated Preferences

• Without bundling: \(P_c = \$1500; P_m = \$600; Profit_{cm} = \$800\)

• With bundling: \(P_b = \$2100; Profit_b = \$800\)

Mixed Bundling

• No Bundling: \(P_c=\$1,300; P_m=\$600; Profits_{cm}=\$1,200\)
• Bundling: \(P_b=\$1,700; Profit_b=\$1,600\)
• Mixed Bundling: \(P_c=\$499; P_m=\$499; Profit_{mix}=\$1798\)

Bundling

• In general, bundling a pair of goods only pays if their demands are negatively correlated

• Customers who are willing to pay relatively more for good A are not willing to pay as much for good B

• The reason is that the price is determined by the purchaser with the lowest reservation price

• If reservation prices for the two goods are negatively correlated, bundling reduces the dispersion of reservation prices and so raises the price at which additional units can be sold

Effects of Advertising

• The firm can capture surplus using nonprice strategies such as advertising

• By advertising, a seller hopes to increase the demand for its product, shifting the demand curve rightward and creating more surplus in the market

• However, advertising is costly.

  • Assume advertising increases fixed costs but not marginal cost of production

Example

Example

• When the firm does not advertise, its maximum profit is areas I + II

• When the firms spends \(A_1\) dollars on advertising, its maximum profit is areas II + III

Monopolist Problem

Firms’ profit-maximization problem on advertising spending

\[ \max_{P,A} PQ(P,A)-C(Q(P,A))-A \]

with \(\frac{dQ}{dP}<0\) and \(\frac{dQ}{dA}\ge0\)

Conditions

For a firm to maximize profit by advertising (expenditure on advertising A > 0) and producing a positive quantity (Q > 0), two conditions must hold:

1. \(MR_Q=MC_Q\), equivalently \(\frac{P-MC_Q}{P}=-\frac{1}{\epsilon_{Q,P}}\)

2. \(MR_A=MC_A\)

Advertising to Sales Ratio

It can be shown that \[ \frac{A}{PQ}=-\frac{\epsilon_{Q,A}}{\epsilon_{Q,P}} \]

• The advertising expenditure share of revenues is equal to the negative ratio of the advertising elasticity of demand to the own price elasticity of demand

• Comparing two markets with the same price elasticity of demand, the advertising-to-sales ratio is higher in the market in which demand is more sensitive to advertising